Suppose $d\not=0$.  We can write $\left(12d+13+14d^2\right)+\left(2d+1\right)$, in the form $ad+b+cd^2$, where $a$, $b$, and $c$ are integers.  Find $a+b+c$.
Solution: Adding the $d$ terms gives us $14d$.  Adding the constant terms gives us $14$.  Adding the $d^2$ terms gives us $14d^2$.  Adding the terms together gives us ${14d+14+14d^2}$, so $a+b+c = \boxed{42}$.